Properties

Label 4029.2.a.k.1.19
Level 4029
Weight 2
Character 4029.1
Self dual yes
Analytic conductor 32.172
Analytic rank 0
Dimension 31
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4029 = 3 \cdot 17 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4029.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(32.1717269744\)
Analytic rank: \(0\)
Dimension: \(31\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.19
Character \(\chi\) = 4029.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.680303 q^{2} +1.00000 q^{3} -1.53719 q^{4} -1.16933 q^{5} +0.680303 q^{6} -3.22223 q^{7} -2.40636 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.680303 q^{2} +1.00000 q^{3} -1.53719 q^{4} -1.16933 q^{5} +0.680303 q^{6} -3.22223 q^{7} -2.40636 q^{8} +1.00000 q^{9} -0.795496 q^{10} -3.38790 q^{11} -1.53719 q^{12} -0.639664 q^{13} -2.19209 q^{14} -1.16933 q^{15} +1.43732 q^{16} +1.00000 q^{17} +0.680303 q^{18} -1.61887 q^{19} +1.79747 q^{20} -3.22223 q^{21} -2.30480 q^{22} +2.39077 q^{23} -2.40636 q^{24} -3.63268 q^{25} -0.435165 q^{26} +1.00000 q^{27} +4.95317 q^{28} -7.67112 q^{29} -0.795496 q^{30} +0.963944 q^{31} +5.79053 q^{32} -3.38790 q^{33} +0.680303 q^{34} +3.76783 q^{35} -1.53719 q^{36} -1.66517 q^{37} -1.10132 q^{38} -0.639664 q^{39} +2.81382 q^{40} +2.74542 q^{41} -2.19209 q^{42} +9.66615 q^{43} +5.20784 q^{44} -1.16933 q^{45} +1.62645 q^{46} +10.9547 q^{47} +1.43732 q^{48} +3.38274 q^{49} -2.47132 q^{50} +1.00000 q^{51} +0.983284 q^{52} -4.10641 q^{53} +0.680303 q^{54} +3.96156 q^{55} +7.75383 q^{56} -1.61887 q^{57} -5.21868 q^{58} -4.30295 q^{59} +1.79747 q^{60} +13.9821 q^{61} +0.655773 q^{62} -3.22223 q^{63} +1.06467 q^{64} +0.747976 q^{65} -2.30480 q^{66} -7.65075 q^{67} -1.53719 q^{68} +2.39077 q^{69} +2.56327 q^{70} +8.73752 q^{71} -2.40636 q^{72} +0.0689540 q^{73} -1.13282 q^{74} -3.63268 q^{75} +2.48851 q^{76} +10.9166 q^{77} -0.435165 q^{78} +1.00000 q^{79} -1.68070 q^{80} +1.00000 q^{81} +1.86772 q^{82} -16.0736 q^{83} +4.95317 q^{84} -1.16933 q^{85} +6.57591 q^{86} -7.67112 q^{87} +8.15251 q^{88} +13.8761 q^{89} -0.795496 q^{90} +2.06114 q^{91} -3.67507 q^{92} +0.963944 q^{93} +7.45252 q^{94} +1.89299 q^{95} +5.79053 q^{96} +0.235021 q^{97} +2.30129 q^{98} -3.38790 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 31q + 4q^{2} + 31q^{3} + 34q^{4} + 11q^{5} + 4q^{6} + 4q^{7} + 12q^{8} + 31q^{9} + O(q^{10}) \) \( 31q + 4q^{2} + 31q^{3} + 34q^{4} + 11q^{5} + 4q^{6} + 4q^{7} + 12q^{8} + 31q^{9} + 5q^{10} + 26q^{11} + 34q^{12} + 7q^{13} + 19q^{14} + 11q^{15} + 40q^{16} + 31q^{17} + 4q^{18} + 32q^{19} + 23q^{20} + 4q^{21} + 2q^{22} + 29q^{23} + 12q^{24} + 32q^{25} + 13q^{26} + 31q^{27} - 13q^{28} + 25q^{29} + 5q^{30} + 22q^{31} + 28q^{32} + 26q^{33} + 4q^{34} + 20q^{35} + 34q^{36} - 4q^{37} + 19q^{38} + 7q^{39} - 3q^{40} + 33q^{41} + 19q^{42} + 6q^{43} + 30q^{44} + 11q^{45} - 11q^{46} + 23q^{47} + 40q^{48} + 31q^{49} + 6q^{50} + 31q^{51} - 7q^{52} + 12q^{53} + 4q^{54} + 40q^{56} + 32q^{57} + 9q^{58} + 27q^{59} + 23q^{60} - 4q^{61} + 25q^{62} + 4q^{63} + 10q^{64} + 54q^{65} + 2q^{66} + 34q^{68} + 29q^{69} - 59q^{70} + 35q^{71} + 12q^{72} + 5q^{73} + 48q^{74} + 32q^{75} + 32q^{76} + 42q^{77} + 13q^{78} + 31q^{79} + 24q^{80} + 31q^{81} + 5q^{82} + 67q^{83} - 13q^{84} + 11q^{85} - 20q^{86} + 25q^{87} - 7q^{88} + 22q^{89} + 5q^{90} + 16q^{91} + 57q^{92} + 22q^{93} + 45q^{94} + 73q^{95} + 28q^{96} - 13q^{97} - 19q^{98} + 26q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.680303 0.481047 0.240523 0.970643i \(-0.422681\pi\)
0.240523 + 0.970643i \(0.422681\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.53719 −0.768594
\(5\) −1.16933 −0.522938 −0.261469 0.965212i \(-0.584207\pi\)
−0.261469 + 0.965212i \(0.584207\pi\)
\(6\) 0.680303 0.277732
\(7\) −3.22223 −1.21789 −0.608944 0.793214i \(-0.708406\pi\)
−0.608944 + 0.793214i \(0.708406\pi\)
\(8\) −2.40636 −0.850776
\(9\) 1.00000 0.333333
\(10\) −0.795496 −0.251558
\(11\) −3.38790 −1.02149 −0.510745 0.859732i \(-0.670631\pi\)
−0.510745 + 0.859732i \(0.670631\pi\)
\(12\) −1.53719 −0.443748
\(13\) −0.639664 −0.177411 −0.0887054 0.996058i \(-0.528273\pi\)
−0.0887054 + 0.996058i \(0.528273\pi\)
\(14\) −2.19209 −0.585860
\(15\) −1.16933 −0.301919
\(16\) 1.43732 0.359331
\(17\) 1.00000 0.242536
\(18\) 0.680303 0.160349
\(19\) −1.61887 −0.371395 −0.185698 0.982607i \(-0.559454\pi\)
−0.185698 + 0.982607i \(0.559454\pi\)
\(20\) 1.79747 0.401927
\(21\) −3.22223 −0.703147
\(22\) −2.30480 −0.491385
\(23\) 2.39077 0.498510 0.249255 0.968438i \(-0.419814\pi\)
0.249255 + 0.968438i \(0.419814\pi\)
\(24\) −2.40636 −0.491196
\(25\) −3.63268 −0.726535
\(26\) −0.435165 −0.0853429
\(27\) 1.00000 0.192450
\(28\) 4.95317 0.936061
\(29\) −7.67112 −1.42449 −0.712245 0.701931i \(-0.752322\pi\)
−0.712245 + 0.701931i \(0.752322\pi\)
\(30\) −0.795496 −0.145237
\(31\) 0.963944 0.173129 0.0865647 0.996246i \(-0.472411\pi\)
0.0865647 + 0.996246i \(0.472411\pi\)
\(32\) 5.79053 1.02363
\(33\) −3.38790 −0.589758
\(34\) 0.680303 0.116671
\(35\) 3.76783 0.636880
\(36\) −1.53719 −0.256198
\(37\) −1.66517 −0.273752 −0.136876 0.990588i \(-0.543706\pi\)
−0.136876 + 0.990588i \(0.543706\pi\)
\(38\) −1.10132 −0.178658
\(39\) −0.639664 −0.102428
\(40\) 2.81382 0.444904
\(41\) 2.74542 0.428762 0.214381 0.976750i \(-0.431227\pi\)
0.214381 + 0.976750i \(0.431227\pi\)
\(42\) −2.19209 −0.338247
\(43\) 9.66615 1.47407 0.737037 0.675852i \(-0.236224\pi\)
0.737037 + 0.675852i \(0.236224\pi\)
\(44\) 5.20784 0.785112
\(45\) −1.16933 −0.174313
\(46\) 1.62645 0.239807
\(47\) 10.9547 1.59791 0.798955 0.601391i \(-0.205387\pi\)
0.798955 + 0.601391i \(0.205387\pi\)
\(48\) 1.43732 0.207460
\(49\) 3.38274 0.483249
\(50\) −2.47132 −0.349497
\(51\) 1.00000 0.140028
\(52\) 0.983284 0.136357
\(53\) −4.10641 −0.564059 −0.282029 0.959406i \(-0.591008\pi\)
−0.282029 + 0.959406i \(0.591008\pi\)
\(54\) 0.680303 0.0925775
\(55\) 3.96156 0.534177
\(56\) 7.75383 1.03615
\(57\) −1.61887 −0.214425
\(58\) −5.21868 −0.685246
\(59\) −4.30295 −0.560197 −0.280098 0.959971i \(-0.590367\pi\)
−0.280098 + 0.959971i \(0.590367\pi\)
\(60\) 1.79747 0.232053
\(61\) 13.9821 1.79022 0.895109 0.445847i \(-0.147097\pi\)
0.895109 + 0.445847i \(0.147097\pi\)
\(62\) 0.655773 0.0832833
\(63\) −3.22223 −0.405962
\(64\) 1.06467 0.133083
\(65\) 0.747976 0.0927749
\(66\) −2.30480 −0.283701
\(67\) −7.65075 −0.934687 −0.467344 0.884076i \(-0.654789\pi\)
−0.467344 + 0.884076i \(0.654789\pi\)
\(68\) −1.53719 −0.186411
\(69\) 2.39077 0.287815
\(70\) 2.56327 0.306369
\(71\) 8.73752 1.03695 0.518476 0.855092i \(-0.326499\pi\)
0.518476 + 0.855092i \(0.326499\pi\)
\(72\) −2.40636 −0.283592
\(73\) 0.0689540 0.00807045 0.00403523 0.999992i \(-0.498716\pi\)
0.00403523 + 0.999992i \(0.498716\pi\)
\(74\) −1.13282 −0.131687
\(75\) −3.63268 −0.419465
\(76\) 2.48851 0.285452
\(77\) 10.9166 1.24406
\(78\) −0.435165 −0.0492727
\(79\) 1.00000 0.112509
\(80\) −1.68070 −0.187908
\(81\) 1.00000 0.111111
\(82\) 1.86772 0.206255
\(83\) −16.0736 −1.76430 −0.882152 0.470964i \(-0.843906\pi\)
−0.882152 + 0.470964i \(0.843906\pi\)
\(84\) 4.95317 0.540435
\(85\) −1.16933 −0.126831
\(86\) 6.57591 0.709099
\(87\) −7.67112 −0.822430
\(88\) 8.15251 0.869060
\(89\) 13.8761 1.47086 0.735432 0.677598i \(-0.236979\pi\)
0.735432 + 0.677598i \(0.236979\pi\)
\(90\) −0.795496 −0.0838526
\(91\) 2.06114 0.216066
\(92\) −3.67507 −0.383152
\(93\) 0.963944 0.0999563
\(94\) 7.45252 0.768669
\(95\) 1.89299 0.194217
\(96\) 5.79053 0.590994
\(97\) 0.235021 0.0238627 0.0119314 0.999929i \(-0.496202\pi\)
0.0119314 + 0.999929i \(0.496202\pi\)
\(98\) 2.30129 0.232465
\(99\) −3.38790 −0.340497
\(100\) 5.58411 0.558411
\(101\) 3.30839 0.329197 0.164598 0.986361i \(-0.447367\pi\)
0.164598 + 0.986361i \(0.447367\pi\)
\(102\) 0.680303 0.0673600
\(103\) −9.76268 −0.961945 −0.480973 0.876736i \(-0.659716\pi\)
−0.480973 + 0.876736i \(0.659716\pi\)
\(104\) 1.53926 0.150937
\(105\) 3.76783 0.367703
\(106\) −2.79360 −0.271339
\(107\) 10.9916 1.06260 0.531301 0.847183i \(-0.321703\pi\)
0.531301 + 0.847183i \(0.321703\pi\)
\(108\) −1.53719 −0.147916
\(109\) 8.50204 0.814348 0.407174 0.913351i \(-0.366514\pi\)
0.407174 + 0.913351i \(0.366514\pi\)
\(110\) 2.69506 0.256964
\(111\) −1.66517 −0.158051
\(112\) −4.63139 −0.437625
\(113\) −2.25201 −0.211852 −0.105926 0.994374i \(-0.533781\pi\)
−0.105926 + 0.994374i \(0.533781\pi\)
\(114\) −1.10132 −0.103148
\(115\) −2.79559 −0.260690
\(116\) 11.7920 1.09486
\(117\) −0.639664 −0.0591369
\(118\) −2.92731 −0.269481
\(119\) −3.22223 −0.295381
\(120\) 2.81382 0.256865
\(121\) 0.477880 0.0434437
\(122\) 9.51203 0.861178
\(123\) 2.74542 0.247546
\(124\) −1.48176 −0.133066
\(125\) 10.0944 0.902872
\(126\) −2.19209 −0.195287
\(127\) 11.9982 1.06467 0.532334 0.846535i \(-0.321315\pi\)
0.532334 + 0.846535i \(0.321315\pi\)
\(128\) −10.8568 −0.959612
\(129\) 9.66615 0.851057
\(130\) 0.508850 0.0446291
\(131\) 1.20920 0.105648 0.0528240 0.998604i \(-0.483178\pi\)
0.0528240 + 0.998604i \(0.483178\pi\)
\(132\) 5.20784 0.453285
\(133\) 5.21638 0.452317
\(134\) −5.20482 −0.449628
\(135\) −1.16933 −0.100640
\(136\) −2.40636 −0.206344
\(137\) 17.4632 1.49198 0.745991 0.665956i \(-0.231976\pi\)
0.745991 + 0.665956i \(0.231976\pi\)
\(138\) 1.62645 0.138452
\(139\) 5.08696 0.431470 0.215735 0.976452i \(-0.430785\pi\)
0.215735 + 0.976452i \(0.430785\pi\)
\(140\) −5.79187 −0.489502
\(141\) 10.9547 0.922554
\(142\) 5.94416 0.498823
\(143\) 2.16712 0.181224
\(144\) 1.43732 0.119777
\(145\) 8.97004 0.744921
\(146\) 0.0469096 0.00388226
\(147\) 3.38274 0.279004
\(148\) 2.55967 0.210404
\(149\) 7.60475 0.623005 0.311503 0.950245i \(-0.399168\pi\)
0.311503 + 0.950245i \(0.399168\pi\)
\(150\) −2.47132 −0.201782
\(151\) −3.93261 −0.320032 −0.160016 0.987114i \(-0.551155\pi\)
−0.160016 + 0.987114i \(0.551155\pi\)
\(152\) 3.89559 0.315974
\(153\) 1.00000 0.0808452
\(154\) 7.42658 0.598451
\(155\) −1.12716 −0.0905360
\(156\) 0.983284 0.0787257
\(157\) 22.6629 1.80870 0.904348 0.426795i \(-0.140357\pi\)
0.904348 + 0.426795i \(0.140357\pi\)
\(158\) 0.680303 0.0541220
\(159\) −4.10641 −0.325659
\(160\) −6.77102 −0.535296
\(161\) −7.70361 −0.607129
\(162\) 0.680303 0.0534496
\(163\) 8.52864 0.668014 0.334007 0.942571i \(-0.391599\pi\)
0.334007 + 0.942571i \(0.391599\pi\)
\(164\) −4.22023 −0.329544
\(165\) 3.96156 0.308407
\(166\) −10.9349 −0.848713
\(167\) −15.5085 −1.20008 −0.600040 0.799970i \(-0.704849\pi\)
−0.600040 + 0.799970i \(0.704849\pi\)
\(168\) 7.75383 0.598221
\(169\) −12.5908 −0.968525
\(170\) −0.795496 −0.0610117
\(171\) −1.61887 −0.123798
\(172\) −14.8587 −1.13297
\(173\) −7.19773 −0.547233 −0.273617 0.961839i \(-0.588220\pi\)
−0.273617 + 0.961839i \(0.588220\pi\)
\(174\) −5.21868 −0.395627
\(175\) 11.7053 0.884838
\(176\) −4.86951 −0.367053
\(177\) −4.30295 −0.323430
\(178\) 9.43995 0.707554
\(179\) 3.71861 0.277942 0.138971 0.990296i \(-0.455621\pi\)
0.138971 + 0.990296i \(0.455621\pi\)
\(180\) 1.79747 0.133976
\(181\) −23.5768 −1.75245 −0.876223 0.481906i \(-0.839945\pi\)
−0.876223 + 0.481906i \(0.839945\pi\)
\(182\) 1.40220 0.103938
\(183\) 13.9821 1.03358
\(184\) −5.75305 −0.424121
\(185\) 1.94712 0.143155
\(186\) 0.655773 0.0480836
\(187\) −3.38790 −0.247748
\(188\) −16.8395 −1.22814
\(189\) −3.22223 −0.234382
\(190\) 1.28781 0.0934274
\(191\) −16.2749 −1.17761 −0.588805 0.808275i \(-0.700402\pi\)
−0.588805 + 0.808275i \(0.700402\pi\)
\(192\) 1.06467 0.0768356
\(193\) 2.68251 0.193091 0.0965457 0.995329i \(-0.469221\pi\)
0.0965457 + 0.995329i \(0.469221\pi\)
\(194\) 0.159885 0.0114791
\(195\) 0.747976 0.0535636
\(196\) −5.19991 −0.371422
\(197\) 18.7273 1.33427 0.667134 0.744938i \(-0.267521\pi\)
0.667134 + 0.744938i \(0.267521\pi\)
\(198\) −2.30480 −0.163795
\(199\) 16.1182 1.14259 0.571295 0.820745i \(-0.306441\pi\)
0.571295 + 0.820745i \(0.306441\pi\)
\(200\) 8.74152 0.618119
\(201\) −7.65075 −0.539642
\(202\) 2.25070 0.158359
\(203\) 24.7181 1.73487
\(204\) −1.53719 −0.107625
\(205\) −3.21029 −0.224216
\(206\) −6.64158 −0.462741
\(207\) 2.39077 0.166170
\(208\) −0.919405 −0.0637492
\(209\) 5.48459 0.379377
\(210\) 2.56327 0.176882
\(211\) 22.2783 1.53370 0.766850 0.641826i \(-0.221823\pi\)
0.766850 + 0.641826i \(0.221823\pi\)
\(212\) 6.31232 0.433532
\(213\) 8.73752 0.598685
\(214\) 7.47764 0.511161
\(215\) −11.3029 −0.770850
\(216\) −2.40636 −0.163732
\(217\) −3.10604 −0.210852
\(218\) 5.78396 0.391739
\(219\) 0.0689540 0.00465948
\(220\) −6.08967 −0.410565
\(221\) −0.639664 −0.0430284
\(222\) −1.13282 −0.0760297
\(223\) −20.2701 −1.35739 −0.678694 0.734421i \(-0.737454\pi\)
−0.678694 + 0.734421i \(0.737454\pi\)
\(224\) −18.6584 −1.24667
\(225\) −3.63268 −0.242178
\(226\) −1.53205 −0.101911
\(227\) 11.9417 0.792596 0.396298 0.918122i \(-0.370295\pi\)
0.396298 + 0.918122i \(0.370295\pi\)
\(228\) 2.48851 0.164806
\(229\) −3.75816 −0.248346 −0.124173 0.992261i \(-0.539628\pi\)
−0.124173 + 0.992261i \(0.539628\pi\)
\(230\) −1.90185 −0.125404
\(231\) 10.9166 0.718259
\(232\) 18.4595 1.21192
\(233\) −16.5382 −1.08346 −0.541728 0.840554i \(-0.682230\pi\)
−0.541728 + 0.840554i \(0.682230\pi\)
\(234\) −0.435165 −0.0284476
\(235\) −12.8096 −0.835608
\(236\) 6.61445 0.430564
\(237\) 1.00000 0.0649570
\(238\) −2.19209 −0.142092
\(239\) −18.7524 −1.21299 −0.606496 0.795086i \(-0.707426\pi\)
−0.606496 + 0.795086i \(0.707426\pi\)
\(240\) −1.68070 −0.108489
\(241\) −0.484078 −0.0311822 −0.0155911 0.999878i \(-0.504963\pi\)
−0.0155911 + 0.999878i \(0.504963\pi\)
\(242\) 0.325103 0.0208984
\(243\) 1.00000 0.0641500
\(244\) −21.4930 −1.37595
\(245\) −3.95553 −0.252709
\(246\) 1.86772 0.119081
\(247\) 1.03554 0.0658895
\(248\) −2.31959 −0.147294
\(249\) −16.0736 −1.01862
\(250\) 6.86726 0.434323
\(251\) −22.7890 −1.43843 −0.719215 0.694787i \(-0.755498\pi\)
−0.719215 + 0.694787i \(0.755498\pi\)
\(252\) 4.95317 0.312020
\(253\) −8.09970 −0.509224
\(254\) 8.16240 0.512155
\(255\) −1.16933 −0.0732260
\(256\) −9.51522 −0.594701
\(257\) 10.5780 0.659839 0.329920 0.944009i \(-0.392978\pi\)
0.329920 + 0.944009i \(0.392978\pi\)
\(258\) 6.57591 0.409398
\(259\) 5.36554 0.333399
\(260\) −1.14978 −0.0713063
\(261\) −7.67112 −0.474830
\(262\) 0.822619 0.0508216
\(263\) 23.0197 1.41946 0.709728 0.704476i \(-0.248818\pi\)
0.709728 + 0.704476i \(0.248818\pi\)
\(264\) 8.15251 0.501752
\(265\) 4.80173 0.294968
\(266\) 3.54872 0.217586
\(267\) 13.8761 0.849204
\(268\) 11.7606 0.718395
\(269\) 22.7666 1.38811 0.694053 0.719924i \(-0.255824\pi\)
0.694053 + 0.719924i \(0.255824\pi\)
\(270\) −0.795496 −0.0484123
\(271\) −2.26550 −0.137620 −0.0688098 0.997630i \(-0.521920\pi\)
−0.0688098 + 0.997630i \(0.521920\pi\)
\(272\) 1.43732 0.0871506
\(273\) 2.06114 0.124746
\(274\) 11.8803 0.717713
\(275\) 12.3072 0.742149
\(276\) −3.67507 −0.221213
\(277\) −14.8072 −0.889679 −0.444839 0.895610i \(-0.646739\pi\)
−0.444839 + 0.895610i \(0.646739\pi\)
\(278\) 3.46067 0.207557
\(279\) 0.963944 0.0577098
\(280\) −9.06676 −0.541842
\(281\) −18.7820 −1.12044 −0.560221 0.828343i \(-0.689284\pi\)
−0.560221 + 0.828343i \(0.689284\pi\)
\(282\) 7.45252 0.443791
\(283\) 27.0646 1.60883 0.804413 0.594071i \(-0.202480\pi\)
0.804413 + 0.594071i \(0.202480\pi\)
\(284\) −13.4312 −0.796996
\(285\) 1.89299 0.112131
\(286\) 1.47430 0.0871770
\(287\) −8.84636 −0.522184
\(288\) 5.79053 0.341210
\(289\) 1.00000 0.0588235
\(290\) 6.10234 0.358342
\(291\) 0.235021 0.0137772
\(292\) −0.105995 −0.00620290
\(293\) −23.5463 −1.37559 −0.687794 0.725906i \(-0.741421\pi\)
−0.687794 + 0.725906i \(0.741421\pi\)
\(294\) 2.30129 0.134214
\(295\) 5.03155 0.292948
\(296\) 4.00699 0.232901
\(297\) −3.38790 −0.196586
\(298\) 5.17353 0.299694
\(299\) −1.52929 −0.0884411
\(300\) 5.58411 0.322399
\(301\) −31.1465 −1.79526
\(302\) −2.67537 −0.153950
\(303\) 3.30839 0.190062
\(304\) −2.32685 −0.133454
\(305\) −16.3496 −0.936174
\(306\) 0.680303 0.0388903
\(307\) −19.6462 −1.12127 −0.560635 0.828063i \(-0.689443\pi\)
−0.560635 + 0.828063i \(0.689443\pi\)
\(308\) −16.7809 −0.956178
\(309\) −9.76268 −0.555379
\(310\) −0.766813 −0.0435520
\(311\) −5.69179 −0.322752 −0.161376 0.986893i \(-0.551593\pi\)
−0.161376 + 0.986893i \(0.551593\pi\)
\(312\) 1.53926 0.0871435
\(313\) −5.20447 −0.294174 −0.147087 0.989124i \(-0.546990\pi\)
−0.147087 + 0.989124i \(0.546990\pi\)
\(314\) 15.4176 0.870068
\(315\) 3.76783 0.212293
\(316\) −1.53719 −0.0864736
\(317\) 14.0120 0.786993 0.393496 0.919326i \(-0.371265\pi\)
0.393496 + 0.919326i \(0.371265\pi\)
\(318\) −2.79360 −0.156657
\(319\) 25.9890 1.45510
\(320\) −1.24494 −0.0695943
\(321\) 10.9916 0.613493
\(322\) −5.24078 −0.292057
\(323\) −1.61887 −0.0900766
\(324\) −1.53719 −0.0853994
\(325\) 2.32369 0.128895
\(326\) 5.80205 0.321346
\(327\) 8.50204 0.470164
\(328\) −6.60646 −0.364781
\(329\) −35.2986 −1.94607
\(330\) 2.69506 0.148358
\(331\) 29.4898 1.62091 0.810453 0.585803i \(-0.199221\pi\)
0.810453 + 0.585803i \(0.199221\pi\)
\(332\) 24.7081 1.35603
\(333\) −1.66517 −0.0912506
\(334\) −10.5504 −0.577295
\(335\) 8.94622 0.488784
\(336\) −4.63139 −0.252663
\(337\) 5.76733 0.314166 0.157083 0.987585i \(-0.449791\pi\)
0.157083 + 0.987585i \(0.449791\pi\)
\(338\) −8.56558 −0.465906
\(339\) −2.25201 −0.122313
\(340\) 1.79747 0.0974817
\(341\) −3.26575 −0.176850
\(342\) −1.10132 −0.0595528
\(343\) 11.6556 0.629344
\(344\) −23.2602 −1.25411
\(345\) −2.79559 −0.150510
\(346\) −4.89664 −0.263245
\(347\) 16.4684 0.884071 0.442036 0.896997i \(-0.354256\pi\)
0.442036 + 0.896997i \(0.354256\pi\)
\(348\) 11.7920 0.632115
\(349\) 9.09941 0.487080 0.243540 0.969891i \(-0.421691\pi\)
0.243540 + 0.969891i \(0.421691\pi\)
\(350\) 7.96315 0.425648
\(351\) −0.639664 −0.0341427
\(352\) −19.6178 −1.04563
\(353\) 16.5448 0.880593 0.440296 0.897852i \(-0.354873\pi\)
0.440296 + 0.897852i \(0.354873\pi\)
\(354\) −2.92731 −0.155585
\(355\) −10.2170 −0.542263
\(356\) −21.3302 −1.13050
\(357\) −3.22223 −0.170538
\(358\) 2.52978 0.133703
\(359\) 7.29846 0.385198 0.192599 0.981278i \(-0.438308\pi\)
0.192599 + 0.981278i \(0.438308\pi\)
\(360\) 2.81382 0.148301
\(361\) −16.3792 −0.862066
\(362\) −16.0393 −0.843008
\(363\) 0.477880 0.0250822
\(364\) −3.16836 −0.166067
\(365\) −0.0806297 −0.00422035
\(366\) 9.51203 0.497202
\(367\) −20.4360 −1.06675 −0.533376 0.845878i \(-0.679077\pi\)
−0.533376 + 0.845878i \(0.679077\pi\)
\(368\) 3.43631 0.179130
\(369\) 2.74542 0.142921
\(370\) 1.32463 0.0688644
\(371\) 13.2318 0.686960
\(372\) −1.48176 −0.0768258
\(373\) −12.2406 −0.633797 −0.316898 0.948460i \(-0.602641\pi\)
−0.316898 + 0.948460i \(0.602641\pi\)
\(374\) −2.30480 −0.119178
\(375\) 10.0944 0.521273
\(376\) −26.3610 −1.35946
\(377\) 4.90694 0.252720
\(378\) −2.19209 −0.112749
\(379\) 10.7197 0.550634 0.275317 0.961353i \(-0.411217\pi\)
0.275317 + 0.961353i \(0.411217\pi\)
\(380\) −2.90988 −0.149274
\(381\) 11.9982 0.614686
\(382\) −11.0719 −0.566486
\(383\) −11.3689 −0.580926 −0.290463 0.956886i \(-0.593809\pi\)
−0.290463 + 0.956886i \(0.593809\pi\)
\(384\) −10.8568 −0.554032
\(385\) −12.7650 −0.650567
\(386\) 1.82492 0.0928860
\(387\) 9.66615 0.491358
\(388\) −0.361271 −0.0183408
\(389\) 14.0806 0.713914 0.356957 0.934121i \(-0.383814\pi\)
0.356957 + 0.934121i \(0.383814\pi\)
\(390\) 0.508850 0.0257666
\(391\) 2.39077 0.120907
\(392\) −8.14009 −0.411137
\(393\) 1.20920 0.0609959
\(394\) 12.7403 0.641845
\(395\) −1.16933 −0.0588352
\(396\) 5.20784 0.261704
\(397\) 0.569760 0.0285954 0.0142977 0.999898i \(-0.495449\pi\)
0.0142977 + 0.999898i \(0.495449\pi\)
\(398\) 10.9653 0.549639
\(399\) 5.21638 0.261146
\(400\) −5.22134 −0.261067
\(401\) −21.4758 −1.07245 −0.536226 0.844074i \(-0.680151\pi\)
−0.536226 + 0.844074i \(0.680151\pi\)
\(402\) −5.20482 −0.259593
\(403\) −0.616600 −0.0307150
\(404\) −5.08561 −0.253019
\(405\) −1.16933 −0.0581043
\(406\) 16.8158 0.834553
\(407\) 5.64142 0.279635
\(408\) −2.40636 −0.119133
\(409\) −24.5365 −1.21325 −0.606626 0.794987i \(-0.707478\pi\)
−0.606626 + 0.794987i \(0.707478\pi\)
\(410\) −2.18397 −0.107859
\(411\) 17.4632 0.861397
\(412\) 15.0071 0.739346
\(413\) 13.8651 0.682256
\(414\) 1.62645 0.0799356
\(415\) 18.7953 0.922623
\(416\) −3.70399 −0.181603
\(417\) 5.08696 0.249109
\(418\) 3.73118 0.182498
\(419\) 13.3456 0.651974 0.325987 0.945374i \(-0.394303\pi\)
0.325987 + 0.945374i \(0.394303\pi\)
\(420\) −5.79187 −0.282614
\(421\) −33.7493 −1.64484 −0.822419 0.568882i \(-0.807376\pi\)
−0.822419 + 0.568882i \(0.807376\pi\)
\(422\) 15.1560 0.737782
\(423\) 10.9547 0.532637
\(424\) 9.88149 0.479888
\(425\) −3.63268 −0.176211
\(426\) 5.94416 0.287995
\(427\) −45.0533 −2.18028
\(428\) −16.8962 −0.816709
\(429\) 2.16712 0.104629
\(430\) −7.68938 −0.370815
\(431\) 1.79289 0.0863606 0.0431803 0.999067i \(-0.486251\pi\)
0.0431803 + 0.999067i \(0.486251\pi\)
\(432\) 1.43732 0.0691533
\(433\) 6.24663 0.300194 0.150097 0.988671i \(-0.452041\pi\)
0.150097 + 0.988671i \(0.452041\pi\)
\(434\) −2.11305 −0.101430
\(435\) 8.97004 0.430080
\(436\) −13.0692 −0.625903
\(437\) −3.87036 −0.185144
\(438\) 0.0469096 0.00224143
\(439\) −32.0645 −1.53036 −0.765178 0.643819i \(-0.777349\pi\)
−0.765178 + 0.643819i \(0.777349\pi\)
\(440\) −9.53294 −0.454465
\(441\) 3.38274 0.161083
\(442\) −0.435165 −0.0206987
\(443\) 37.4856 1.78099 0.890497 0.454989i \(-0.150357\pi\)
0.890497 + 0.454989i \(0.150357\pi\)
\(444\) 2.55967 0.121477
\(445\) −16.2257 −0.769172
\(446\) −13.7898 −0.652967
\(447\) 7.60475 0.359692
\(448\) −3.43059 −0.162080
\(449\) 14.4890 0.683777 0.341888 0.939741i \(-0.388934\pi\)
0.341888 + 0.939741i \(0.388934\pi\)
\(450\) −2.47132 −0.116499
\(451\) −9.30121 −0.437977
\(452\) 3.46177 0.162828
\(453\) −3.93261 −0.184770
\(454\) 8.12395 0.381276
\(455\) −2.41015 −0.112989
\(456\) 3.89559 0.182428
\(457\) 7.59012 0.355051 0.177525 0.984116i \(-0.443191\pi\)
0.177525 + 0.984116i \(0.443191\pi\)
\(458\) −2.55668 −0.119466
\(459\) 1.00000 0.0466760
\(460\) 4.29735 0.200365
\(461\) 6.83207 0.318201 0.159101 0.987262i \(-0.449141\pi\)
0.159101 + 0.987262i \(0.449141\pi\)
\(462\) 7.42658 0.345516
\(463\) −10.6639 −0.495595 −0.247797 0.968812i \(-0.579707\pi\)
−0.247797 + 0.968812i \(0.579707\pi\)
\(464\) −11.0259 −0.511864
\(465\) −1.12716 −0.0522710
\(466\) −11.2510 −0.521192
\(467\) 6.42530 0.297327 0.148664 0.988888i \(-0.452503\pi\)
0.148664 + 0.988888i \(0.452503\pi\)
\(468\) 0.983284 0.0454523
\(469\) 24.6524 1.13834
\(470\) −8.71443 −0.401967
\(471\) 22.6629 1.04425
\(472\) 10.3544 0.476602
\(473\) −32.7480 −1.50575
\(474\) 0.680303 0.0312473
\(475\) 5.88085 0.269832
\(476\) 4.95317 0.227028
\(477\) −4.10641 −0.188020
\(478\) −12.7573 −0.583506
\(479\) −16.7896 −0.767135 −0.383568 0.923513i \(-0.625305\pi\)
−0.383568 + 0.923513i \(0.625305\pi\)
\(480\) −6.77102 −0.309053
\(481\) 1.06515 0.0485665
\(482\) −0.329319 −0.0150001
\(483\) −7.70361 −0.350526
\(484\) −0.734592 −0.0333906
\(485\) −0.274816 −0.0124787
\(486\) 0.680303 0.0308592
\(487\) 4.90747 0.222379 0.111189 0.993799i \(-0.464534\pi\)
0.111189 + 0.993799i \(0.464534\pi\)
\(488\) −33.6458 −1.52308
\(489\) 8.52864 0.385678
\(490\) −2.69096 −0.121565
\(491\) 36.2132 1.63428 0.817139 0.576440i \(-0.195559\pi\)
0.817139 + 0.576440i \(0.195559\pi\)
\(492\) −4.22023 −0.190263
\(493\) −7.67112 −0.345490
\(494\) 0.704477 0.0316959
\(495\) 3.96156 0.178059
\(496\) 1.38550 0.0622108
\(497\) −28.1543 −1.26289
\(498\) −10.9349 −0.490005
\(499\) 18.1662 0.813231 0.406616 0.913599i \(-0.366709\pi\)
0.406616 + 0.913599i \(0.366709\pi\)
\(500\) −15.5170 −0.693942
\(501\) −15.5085 −0.692867
\(502\) −15.5034 −0.691952
\(503\) 15.8740 0.707786 0.353893 0.935286i \(-0.384858\pi\)
0.353893 + 0.935286i \(0.384858\pi\)
\(504\) 7.75383 0.345383
\(505\) −3.86858 −0.172150
\(506\) −5.51025 −0.244960
\(507\) −12.5908 −0.559178
\(508\) −18.4435 −0.818297
\(509\) −0.637468 −0.0282553 −0.0141276 0.999900i \(-0.504497\pi\)
−0.0141276 + 0.999900i \(0.504497\pi\)
\(510\) −0.795496 −0.0352251
\(511\) −0.222185 −0.00982890
\(512\) 15.2403 0.673533
\(513\) −1.61887 −0.0714750
\(514\) 7.19626 0.317413
\(515\) 11.4158 0.503038
\(516\) −14.8587 −0.654118
\(517\) −37.1135 −1.63225
\(518\) 3.65019 0.160380
\(519\) −7.19773 −0.315945
\(520\) −1.79990 −0.0789307
\(521\) 15.6632 0.686219 0.343109 0.939295i \(-0.388520\pi\)
0.343109 + 0.939295i \(0.388520\pi\)
\(522\) −5.21868 −0.228415
\(523\) −25.2970 −1.10616 −0.553081 0.833128i \(-0.686548\pi\)
−0.553081 + 0.833128i \(0.686548\pi\)
\(524\) −1.85876 −0.0812004
\(525\) 11.7053 0.510861
\(526\) 15.6604 0.682825
\(527\) 0.963944 0.0419900
\(528\) −4.86951 −0.211918
\(529\) −17.2842 −0.751488
\(530\) 3.26663 0.141893
\(531\) −4.30295 −0.186732
\(532\) −8.01856 −0.347649
\(533\) −1.75615 −0.0760671
\(534\) 9.43995 0.408507
\(535\) −12.8528 −0.555675
\(536\) 18.4104 0.795210
\(537\) 3.71861 0.160470
\(538\) 15.4882 0.667743
\(539\) −11.4604 −0.493634
\(540\) 1.79747 0.0773510
\(541\) −10.5568 −0.453873 −0.226937 0.973910i \(-0.572871\pi\)
−0.226937 + 0.973910i \(0.572871\pi\)
\(542\) −1.54123 −0.0662014
\(543\) −23.5768 −1.01178
\(544\) 5.79053 0.248267
\(545\) −9.94166 −0.425854
\(546\) 1.40220 0.0600086
\(547\) −6.33274 −0.270768 −0.135384 0.990793i \(-0.543227\pi\)
−0.135384 + 0.990793i \(0.543227\pi\)
\(548\) −26.8442 −1.14673
\(549\) 13.9821 0.596739
\(550\) 8.37259 0.357008
\(551\) 12.4186 0.529049
\(552\) −5.75305 −0.244866
\(553\) −3.22223 −0.137023
\(554\) −10.0734 −0.427977
\(555\) 1.94712 0.0826507
\(556\) −7.81961 −0.331625
\(557\) −29.2840 −1.24080 −0.620401 0.784284i \(-0.713030\pi\)
−0.620401 + 0.784284i \(0.713030\pi\)
\(558\) 0.655773 0.0277611
\(559\) −6.18309 −0.261517
\(560\) 5.41560 0.228851
\(561\) −3.38790 −0.143037
\(562\) −12.7775 −0.538985
\(563\) 42.6336 1.79679 0.898395 0.439188i \(-0.144734\pi\)
0.898395 + 0.439188i \(0.144734\pi\)
\(564\) −16.8395 −0.709069
\(565\) 2.63334 0.110785
\(566\) 18.4121 0.773920
\(567\) −3.22223 −0.135321
\(568\) −21.0256 −0.882215
\(569\) 13.0174 0.545716 0.272858 0.962054i \(-0.412031\pi\)
0.272858 + 0.962054i \(0.412031\pi\)
\(570\) 1.28781 0.0539403
\(571\) 15.1453 0.633813 0.316906 0.948457i \(-0.397356\pi\)
0.316906 + 0.948457i \(0.397356\pi\)
\(572\) −3.33127 −0.139287
\(573\) −16.2749 −0.679894
\(574\) −6.01820 −0.251195
\(575\) −8.68490 −0.362185
\(576\) 1.06467 0.0443611
\(577\) −11.9103 −0.495831 −0.247915 0.968782i \(-0.579746\pi\)
−0.247915 + 0.968782i \(0.579746\pi\)
\(578\) 0.680303 0.0282969
\(579\) 2.68251 0.111481
\(580\) −13.7886 −0.572542
\(581\) 51.7927 2.14872
\(582\) 0.159885 0.00662746
\(583\) 13.9121 0.576181
\(584\) −0.165928 −0.00686615
\(585\) 0.747976 0.0309250
\(586\) −16.0186 −0.661722
\(587\) 26.1646 1.07993 0.539964 0.841688i \(-0.318438\pi\)
0.539964 + 0.841688i \(0.318438\pi\)
\(588\) −5.19991 −0.214441
\(589\) −1.56050 −0.0642994
\(590\) 3.42298 0.140922
\(591\) 18.7273 0.770340
\(592\) −2.39338 −0.0983675
\(593\) 30.1410 1.23774 0.618870 0.785493i \(-0.287591\pi\)
0.618870 + 0.785493i \(0.287591\pi\)
\(594\) −2.30480 −0.0945670
\(595\) 3.76783 0.154466
\(596\) −11.6899 −0.478838
\(597\) 16.1182 0.659675
\(598\) −1.04038 −0.0425443
\(599\) −33.3322 −1.36192 −0.680959 0.732321i \(-0.738437\pi\)
−0.680959 + 0.732321i \(0.738437\pi\)
\(600\) 8.74152 0.356871
\(601\) 45.7955 1.86804 0.934019 0.357224i \(-0.116277\pi\)
0.934019 + 0.357224i \(0.116277\pi\)
\(602\) −21.1891 −0.863602
\(603\) −7.65075 −0.311562
\(604\) 6.04517 0.245974
\(605\) −0.558798 −0.0227184
\(606\) 2.25070 0.0914286
\(607\) −6.33341 −0.257065 −0.128533 0.991705i \(-0.541027\pi\)
−0.128533 + 0.991705i \(0.541027\pi\)
\(608\) −9.37414 −0.380172
\(609\) 24.7181 1.00163
\(610\) −11.1227 −0.450343
\(611\) −7.00734 −0.283486
\(612\) −1.53719 −0.0621372
\(613\) −41.3477 −1.67002 −0.835009 0.550237i \(-0.814537\pi\)
−0.835009 + 0.550237i \(0.814537\pi\)
\(614\) −13.3654 −0.539383
\(615\) −3.21029 −0.129451
\(616\) −26.2692 −1.05842
\(617\) 42.4698 1.70977 0.854885 0.518818i \(-0.173628\pi\)
0.854885 + 0.518818i \(0.173628\pi\)
\(618\) −6.64158 −0.267163
\(619\) 2.58275 0.103809 0.0519047 0.998652i \(-0.483471\pi\)
0.0519047 + 0.998652i \(0.483471\pi\)
\(620\) 1.73266 0.0695855
\(621\) 2.39077 0.0959383
\(622\) −3.87214 −0.155259
\(623\) −44.7120 −1.79135
\(624\) −0.919405 −0.0368056
\(625\) 6.35973 0.254389
\(626\) −3.54062 −0.141512
\(627\) 5.48459 0.219033
\(628\) −34.8372 −1.39015
\(629\) −1.66517 −0.0663945
\(630\) 2.56327 0.102123
\(631\) 9.38046 0.373430 0.186715 0.982414i \(-0.440216\pi\)
0.186715 + 0.982414i \(0.440216\pi\)
\(632\) −2.40636 −0.0957198
\(633\) 22.2783 0.885483
\(634\) 9.53241 0.378580
\(635\) −14.0298 −0.556756
\(636\) 6.31232 0.250300
\(637\) −2.16382 −0.0857336
\(638\) 17.6804 0.699973
\(639\) 8.73752 0.345651
\(640\) 12.6951 0.501818
\(641\) 11.1827 0.441689 0.220845 0.975309i \(-0.429119\pi\)
0.220845 + 0.975309i \(0.429119\pi\)
\(642\) 7.47764 0.295119
\(643\) 12.3598 0.487425 0.243712 0.969848i \(-0.421635\pi\)
0.243712 + 0.969848i \(0.421635\pi\)
\(644\) 11.8419 0.466636
\(645\) −11.3029 −0.445051
\(646\) −1.10132 −0.0433310
\(647\) 30.7435 1.20865 0.604325 0.796738i \(-0.293443\pi\)
0.604325 + 0.796738i \(0.293443\pi\)
\(648\) −2.40636 −0.0945307
\(649\) 14.5780 0.572236
\(650\) 1.58081 0.0620046
\(651\) −3.10604 −0.121735
\(652\) −13.1101 −0.513432
\(653\) 14.6447 0.573091 0.286545 0.958067i \(-0.407493\pi\)
0.286545 + 0.958067i \(0.407493\pi\)
\(654\) 5.78396 0.226171
\(655\) −1.41394 −0.0552474
\(656\) 3.94606 0.154068
\(657\) 0.0689540 0.00269015
\(658\) −24.0137 −0.936152
\(659\) 44.0204 1.71479 0.857395 0.514658i \(-0.172081\pi\)
0.857395 + 0.514658i \(0.172081\pi\)
\(660\) −6.08967 −0.237040
\(661\) −22.4397 −0.872804 −0.436402 0.899752i \(-0.643747\pi\)
−0.436402 + 0.899752i \(0.643747\pi\)
\(662\) 20.0620 0.779732
\(663\) −0.639664 −0.0248425
\(664\) 38.6788 1.50103
\(665\) −6.09965 −0.236534
\(666\) −1.13282 −0.0438958
\(667\) −18.3399 −0.710123
\(668\) 23.8394 0.922375
\(669\) −20.2701 −0.783688
\(670\) 6.08613 0.235128
\(671\) −47.3698 −1.82869
\(672\) −18.6584 −0.719764
\(673\) −20.5139 −0.790752 −0.395376 0.918519i \(-0.629386\pi\)
−0.395376 + 0.918519i \(0.629386\pi\)
\(674\) 3.92353 0.151129
\(675\) −3.63268 −0.139822
\(676\) 19.3545 0.744403
\(677\) −2.56261 −0.0984890 −0.0492445 0.998787i \(-0.515681\pi\)
−0.0492445 + 0.998787i \(0.515681\pi\)
\(678\) −1.53205 −0.0588381
\(679\) −0.757290 −0.0290621
\(680\) 2.81382 0.107905
\(681\) 11.9417 0.457606
\(682\) −2.22170 −0.0850731
\(683\) 12.7959 0.489620 0.244810 0.969571i \(-0.421274\pi\)
0.244810 + 0.969571i \(0.421274\pi\)
\(684\) 2.48851 0.0951507
\(685\) −20.4202 −0.780215
\(686\) 7.92935 0.302744
\(687\) −3.75816 −0.143383
\(688\) 13.8934 0.529681
\(689\) 2.62672 0.100070
\(690\) −1.90185 −0.0724021
\(691\) −6.05582 −0.230374 −0.115187 0.993344i \(-0.536747\pi\)
−0.115187 + 0.993344i \(0.536747\pi\)
\(692\) 11.0643 0.420600
\(693\) 10.9166 0.414687
\(694\) 11.2035 0.425280
\(695\) −5.94831 −0.225632
\(696\) 18.4595 0.699704
\(697\) 2.74542 0.103990
\(698\) 6.19035 0.234308
\(699\) −16.5382 −0.625533
\(700\) −17.9933 −0.680081
\(701\) 12.0305 0.454384 0.227192 0.973850i \(-0.427045\pi\)
0.227192 + 0.973850i \(0.427045\pi\)
\(702\) −0.435165 −0.0164242
\(703\) 2.69570 0.101670
\(704\) −3.60698 −0.135943
\(705\) −12.8096 −0.482439
\(706\) 11.2555 0.423606
\(707\) −10.6604 −0.400925
\(708\) 6.61445 0.248586
\(709\) −27.8892 −1.04740 −0.523701 0.851902i \(-0.675449\pi\)
−0.523701 + 0.851902i \(0.675449\pi\)
\(710\) −6.95066 −0.260854
\(711\) 1.00000 0.0375029
\(712\) −33.3909 −1.25138
\(713\) 2.30457 0.0863068
\(714\) −2.19209 −0.0820369
\(715\) −2.53407 −0.0947688
\(716\) −5.71620 −0.213624
\(717\) −18.7524 −0.700322
\(718\) 4.96516 0.185298
\(719\) 37.8614 1.41199 0.705997 0.708215i \(-0.250499\pi\)
0.705997 + 0.708215i \(0.250499\pi\)
\(720\) −1.68070 −0.0626360
\(721\) 31.4576 1.17154
\(722\) −11.1428 −0.414694
\(723\) −0.484078 −0.0180030
\(724\) 36.2419 1.34692
\(725\) 27.8667 1.03494
\(726\) 0.325103 0.0120657
\(727\) 2.72586 0.101096 0.0505482 0.998722i \(-0.483903\pi\)
0.0505482 + 0.998722i \(0.483903\pi\)
\(728\) −4.95985 −0.183824
\(729\) 1.00000 0.0370370
\(730\) −0.0548526 −0.00203018
\(731\) 9.66615 0.357516
\(732\) −21.4930 −0.794406
\(733\) 1.84593 0.0681811 0.0340906 0.999419i \(-0.489147\pi\)
0.0340906 + 0.999419i \(0.489147\pi\)
\(734\) −13.9027 −0.513158
\(735\) −3.95553 −0.145902
\(736\) 13.8438 0.510291
\(737\) 25.9200 0.954775
\(738\) 1.86772 0.0687516
\(739\) −1.52241 −0.0560027 −0.0280013 0.999608i \(-0.508914\pi\)
−0.0280013 + 0.999608i \(0.508914\pi\)
\(740\) −2.99309 −0.110028
\(741\) 1.03554 0.0380413
\(742\) 9.00162 0.330460
\(743\) −14.2263 −0.521913 −0.260957 0.965351i \(-0.584038\pi\)
−0.260957 + 0.965351i \(0.584038\pi\)
\(744\) −2.31959 −0.0850405
\(745\) −8.89243 −0.325793
\(746\) −8.32734 −0.304886
\(747\) −16.0736 −0.588102
\(748\) 5.20784 0.190418
\(749\) −35.4175 −1.29413
\(750\) 6.86726 0.250757
\(751\) −6.73917 −0.245916 −0.122958 0.992412i \(-0.539238\pi\)
−0.122958 + 0.992412i \(0.539238\pi\)
\(752\) 15.7455 0.574179
\(753\) −22.7890 −0.830478
\(754\) 3.33820 0.121570
\(755\) 4.59851 0.167357
\(756\) 4.95317 0.180145
\(757\) 47.4866 1.72593 0.862964 0.505265i \(-0.168605\pi\)
0.862964 + 0.505265i \(0.168605\pi\)
\(758\) 7.29264 0.264881
\(759\) −8.09970 −0.294000
\(760\) −4.55522 −0.165235
\(761\) −20.2771 −0.735045 −0.367522 0.930015i \(-0.619794\pi\)
−0.367522 + 0.930015i \(0.619794\pi\)
\(762\) 8.16240 0.295693
\(763\) −27.3955 −0.991784
\(764\) 25.0176 0.905105
\(765\) −1.16933 −0.0422771
\(766\) −7.73432 −0.279452
\(767\) 2.75244 0.0993850
\(768\) −9.51522 −0.343351
\(769\) 14.3996 0.519261 0.259631 0.965708i \(-0.416399\pi\)
0.259631 + 0.965708i \(0.416399\pi\)
\(770\) −8.68410 −0.312953
\(771\) 10.5780 0.380958
\(772\) −4.12353 −0.148409
\(773\) 10.7101 0.385215 0.192607 0.981276i \(-0.438306\pi\)
0.192607 + 0.981276i \(0.438306\pi\)
\(774\) 6.57591 0.236366
\(775\) −3.50170 −0.125785
\(776\) −0.565544 −0.0203019
\(777\) 5.36554 0.192488
\(778\) 9.57905 0.343426
\(779\) −4.44449 −0.159240
\(780\) −1.14978 −0.0411687
\(781\) −29.6019 −1.05924
\(782\) 1.62645 0.0581617
\(783\) −7.67112 −0.274143
\(784\) 4.86210 0.173646
\(785\) −26.5003 −0.945837
\(786\) 0.822619 0.0293418
\(787\) 33.7288 1.20230 0.601150 0.799136i \(-0.294709\pi\)
0.601150 + 0.799136i \(0.294709\pi\)
\(788\) −28.7874 −1.02551
\(789\) 23.0197 0.819524
\(790\) −0.795496 −0.0283025
\(791\) 7.25650 0.258011
\(792\) 8.15251 0.289687
\(793\) −8.94381 −0.317604
\(794\) 0.387609 0.0137557
\(795\) 4.80173 0.170300
\(796\) −24.7767 −0.878188
\(797\) −15.7768 −0.558845 −0.279422 0.960168i \(-0.590143\pi\)
−0.279422 + 0.960168i \(0.590143\pi\)
\(798\) 3.54872 0.125623
\(799\) 10.9547 0.387550
\(800\) −21.0351 −0.743704
\(801\) 13.8761 0.490288
\(802\) −14.6101 −0.515900
\(803\) −0.233609 −0.00824389
\(804\) 11.7606 0.414766
\(805\) 9.00803 0.317491
\(806\) −0.419475 −0.0147754
\(807\) 22.7666 0.801423
\(808\) −7.96116 −0.280073
\(809\) −35.0687 −1.23295 −0.616475 0.787374i \(-0.711440\pi\)
−0.616475 + 0.787374i \(0.711440\pi\)
\(810\) −0.795496 −0.0279509
\(811\) −24.1664 −0.848597 −0.424298 0.905522i \(-0.639479\pi\)
−0.424298 + 0.905522i \(0.639479\pi\)
\(812\) −37.9963 −1.33341
\(813\) −2.26550 −0.0794547
\(814\) 3.83787 0.134517
\(815\) −9.97275 −0.349330
\(816\) 1.43732 0.0503164
\(817\) −15.6483 −0.547464
\(818\) −16.6923 −0.583631
\(819\) 2.06114 0.0720221
\(820\) 4.93482 0.172331
\(821\) −2.32220 −0.0810452 −0.0405226 0.999179i \(-0.512902\pi\)
−0.0405226 + 0.999179i \(0.512902\pi\)
\(822\) 11.8803 0.414372
\(823\) −56.3300 −1.96354 −0.981771 0.190069i \(-0.939129\pi\)
−0.981771 + 0.190069i \(0.939129\pi\)
\(824\) 23.4925 0.818400
\(825\) 12.3072 0.428480
\(826\) 9.43246 0.328197
\(827\) 7.78244 0.270622 0.135311 0.990803i \(-0.456797\pi\)
0.135311 + 0.990803i \(0.456797\pi\)
\(828\) −3.67507 −0.127717
\(829\) −25.0005 −0.868304 −0.434152 0.900840i \(-0.642952\pi\)
−0.434152 + 0.900840i \(0.642952\pi\)
\(830\) 12.7865 0.443825
\(831\) −14.8072 −0.513656
\(832\) −0.681028 −0.0236104
\(833\) 3.38274 0.117205
\(834\) 3.46067 0.119833
\(835\) 18.1344 0.627568
\(836\) −8.43084 −0.291587
\(837\) 0.963944 0.0333188
\(838\) 9.07904 0.313630
\(839\) −16.2981 −0.562674 −0.281337 0.959609i \(-0.590778\pi\)
−0.281337 + 0.959609i \(0.590778\pi\)
\(840\) −9.06676 −0.312833
\(841\) 29.8460 1.02917
\(842\) −22.9597 −0.791244
\(843\) −18.7820 −0.646887
\(844\) −34.2459 −1.17879
\(845\) 14.7228 0.506479
\(846\) 7.45252 0.256223
\(847\) −1.53984 −0.0529095
\(848\) −5.90224 −0.202684
\(849\) 27.0646 0.928856
\(850\) −2.47132 −0.0847656
\(851\) −3.98103 −0.136468
\(852\) −13.4312 −0.460146
\(853\) 11.9132 0.407902 0.203951 0.978981i \(-0.434622\pi\)
0.203951 + 0.978981i \(0.434622\pi\)
\(854\) −30.6499 −1.04882
\(855\) 1.89299 0.0647389
\(856\) −26.4498 −0.904036
\(857\) −19.8048 −0.676518 −0.338259 0.941053i \(-0.609838\pi\)
−0.338259 + 0.941053i \(0.609838\pi\)
\(858\) 1.47430 0.0503316
\(859\) 38.4594 1.31222 0.656109 0.754666i \(-0.272201\pi\)
0.656109 + 0.754666i \(0.272201\pi\)
\(860\) 17.3747 0.592471
\(861\) −8.84636 −0.301483
\(862\) 1.21971 0.0415435
\(863\) 23.0904 0.786005 0.393003 0.919537i \(-0.371436\pi\)
0.393003 + 0.919537i \(0.371436\pi\)
\(864\) 5.79053 0.196998
\(865\) 8.41649 0.286169
\(866\) 4.24960 0.144407
\(867\) 1.00000 0.0339618
\(868\) 4.77458 0.162060
\(869\) −3.38790 −0.114927
\(870\) 6.10234 0.206889
\(871\) 4.89391 0.165824
\(872\) −20.4590 −0.692828
\(873\) 0.235021 0.00795425
\(874\) −2.63301 −0.0890631
\(875\) −32.5265 −1.09960
\(876\) −0.105995 −0.00358125
\(877\) 30.8283 1.04100 0.520499 0.853863i \(-0.325746\pi\)
0.520499 + 0.853863i \(0.325746\pi\)
\(878\) −21.8136 −0.736172
\(879\) −23.5463 −0.794196
\(880\) 5.69405 0.191946
\(881\) 33.4394 1.12660 0.563302 0.826251i \(-0.309531\pi\)
0.563302 + 0.826251i \(0.309531\pi\)
\(882\) 2.30129 0.0774884
\(883\) −29.0856 −0.978809 −0.489404 0.872057i \(-0.662786\pi\)
−0.489404 + 0.872057i \(0.662786\pi\)
\(884\) 0.983284 0.0330714
\(885\) 5.03155 0.169134
\(886\) 25.5015 0.856741
\(887\) 4.97834 0.167156 0.0835782 0.996501i \(-0.473365\pi\)
0.0835782 + 0.996501i \(0.473365\pi\)
\(888\) 4.00699 0.134466
\(889\) −38.6609 −1.29664
\(890\) −11.0384 −0.370007
\(891\) −3.38790 −0.113499
\(892\) 31.1590 1.04328
\(893\) −17.7343 −0.593456
\(894\) 5.17353 0.173029
\(895\) −4.34826 −0.145346
\(896\) 34.9830 1.16870
\(897\) −1.52929 −0.0510615
\(898\) 9.85688 0.328928
\(899\) −7.39453 −0.246621
\(900\) 5.58411 0.186137
\(901\) −4.10641 −0.136804
\(902\) −6.32764 −0.210687
\(903\) −31.1465 −1.03649
\(904\) 5.41915 0.180238
\(905\) 27.5689 0.916421
\(906\) −2.67537 −0.0888831
\(907\) −6.39323 −0.212284 −0.106142 0.994351i \(-0.533850\pi\)
−0.106142 + 0.994351i \(0.533850\pi\)
\(908\) −18.3566 −0.609185
\(909\) 3.30839 0.109732
\(910\) −1.63963 −0.0543532
\(911\) −5.54669 −0.183770 −0.0918849 0.995770i \(-0.529289\pi\)
−0.0918849 + 0.995770i \(0.529289\pi\)
\(912\) −2.32685 −0.0770496
\(913\) 54.4557 1.80222
\(914\) 5.16358 0.170796
\(915\) −16.3496 −0.540500
\(916\) 5.77699 0.190877
\(917\) −3.89630 −0.128667
\(918\) 0.680303 0.0224533
\(919\) 36.6534 1.20908 0.604542 0.796573i \(-0.293356\pi\)
0.604542 + 0.796573i \(0.293356\pi\)
\(920\) 6.72719 0.221789
\(921\) −19.6462 −0.647365
\(922\) 4.64787 0.153070
\(923\) −5.58908 −0.183967
\(924\) −16.7809 −0.552049
\(925\) 6.04901 0.198890
\(926\) −7.25470 −0.238404
\(927\) −9.76268 −0.320648
\(928\) −44.4199 −1.45815
\(929\) 36.4348 1.19539 0.597693 0.801725i \(-0.296084\pi\)
0.597693 + 0.801725i \(0.296084\pi\)
\(930\) −0.766813 −0.0251448
\(931\) −5.47623 −0.179476
\(932\) 25.4224 0.832737
\(933\) −5.69179 −0.186341
\(934\) 4.37115 0.143028
\(935\) 3.96156 0.129557
\(936\) 1.53926 0.0503123
\(937\) 6.50428 0.212485 0.106243 0.994340i \(-0.466118\pi\)
0.106243 + 0.994340i \(0.466118\pi\)
\(938\) 16.7711 0.547596
\(939\) −5.20447 −0.169842
\(940\) 19.6908 0.642244
\(941\) −19.8395 −0.646749 −0.323374 0.946271i \(-0.604817\pi\)
−0.323374 + 0.946271i \(0.604817\pi\)
\(942\) 15.4176 0.502334
\(943\) 6.56367 0.213742
\(944\) −6.18474 −0.201296
\(945\) 3.76783 0.122568
\(946\) −22.2785 −0.724338
\(947\) −18.3063 −0.594874 −0.297437 0.954741i \(-0.596132\pi\)
−0.297437 + 0.954741i \(0.596132\pi\)
\(948\) −1.53719 −0.0499256
\(949\) −0.0441074 −0.00143179
\(950\) 4.00076 0.129802
\(951\) 14.0120 0.454371
\(952\) 7.75383 0.251303
\(953\) −3.89728 −0.126245 −0.0631226 0.998006i \(-0.520106\pi\)
−0.0631226 + 0.998006i \(0.520106\pi\)
\(954\) −2.79360 −0.0904462
\(955\) 19.0307 0.615818
\(956\) 28.8260 0.932299
\(957\) 25.9890 0.840105
\(958\) −11.4220 −0.369028
\(959\) −56.2704 −1.81707
\(960\) −1.24494 −0.0401803
\(961\) −30.0708 −0.970026
\(962\) 0.724622 0.0233628
\(963\) 10.9916 0.354200
\(964\) 0.744119 0.0239664
\(965\) −3.13673 −0.100975
\(966\) −5.24078 −0.168619
\(967\) −57.8586 −1.86061 −0.930304 0.366790i \(-0.880457\pi\)
−0.930304 + 0.366790i \(0.880457\pi\)
\(968\) −1.14995 −0.0369608
\(969\) −1.61887 −0.0520057
\(970\) −0.186958 −0.00600286
\(971\) 1.86291 0.0597837 0.0298919 0.999553i \(-0.490484\pi\)
0.0298919 + 0.999553i \(0.490484\pi\)
\(972\) −1.53719 −0.0493053
\(973\) −16.3913 −0.525482
\(974\) 3.33856 0.106974
\(975\) 2.32369 0.0744177
\(976\) 20.0967 0.643281
\(977\) 17.7417 0.567608 0.283804 0.958882i \(-0.408403\pi\)
0.283804 + 0.958882i \(0.408403\pi\)
\(978\) 5.80205 0.185529
\(979\) −47.0109 −1.50247
\(980\) 6.08039 0.194231
\(981\) 8.50204 0.271449
\(982\) 24.6359 0.786164
\(983\) 2.31533 0.0738476 0.0369238 0.999318i \(-0.488244\pi\)
0.0369238 + 0.999318i \(0.488244\pi\)
\(984\) −6.60646 −0.210606
\(985\) −21.8984 −0.697740
\(986\) −5.21868 −0.166197
\(987\) −35.2986 −1.12357
\(988\) −1.59181 −0.0506423
\(989\) 23.1096 0.734841
\(990\) 2.69506 0.0856547
\(991\) 11.1529 0.354285 0.177142 0.984185i \(-0.443315\pi\)
0.177142 + 0.984185i \(0.443315\pi\)
\(992\) 5.58175 0.177221
\(993\) 29.4898 0.935831
\(994\) −19.1534 −0.607510
\(995\) −18.8474 −0.597504
\(996\) 24.7081 0.782907
\(997\) −23.6499 −0.749000 −0.374500 0.927227i \(-0.622186\pi\)
−0.374500 + 0.927227i \(0.622186\pi\)
\(998\) 12.3585 0.391202
\(999\) −1.66517 −0.0526835
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 4029.2.a.k.1.19 31
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4029.2.a.k.1.19 31 1.1 even 1 trivial